Ribbon-moves of 2-knots: the Farber-Levine pairing and the Atiyah-Patodi-Singer-Casson-Gordon-Ruberman $\widetildeη$-invariants of 2-knots

Eiji Ogasa

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Ribbon-moves of 2-knots: the Farber-Levine pairing and the Atiyah-Patodi-Singer-Casson-Gordon-Ruberman $\widetildeη$-invariants of 2-knots

Eiji Ogasa

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Abstract

Let K and K' be 2-knots. Suppose that K and K' are ribbon-move equivalent. Then the Farber-Levine pairing for K is equivalent to that for K' and the (Z-)torsion part of the first Alexander module of $K$ is isomorphic to that of K' as Z[Z] modules. Let K be a 2-knot which is ribbon-move equivalent to the trivial knot. Then the Atiyah-Patodi-Singer-Casson-Gordon-Ruberman Q/Z-valued \widetildeη-invariants of K for Z_d is zero. (d is a natural number. d>2.).

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Eiji Ogasa. 2000-04-02. Ribbon-moves of 2-knots: the Farber-Levine pairing and the Atiyah-Patodi-Singer-Casson-Gordon-Ruberman $\widetildeη$-invariants of 2-knots. https://arxiv.org/abs/math/0004007

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